Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces

Volume 201 / 2010

Catalin Badea, Yuri I. Lyubich Studia Mathematica 201 (2010), 21-35 MSC: Primary 47A05; Secondary 46B20, 47A10. DOI: 10.4064/sm201-1-2

Abstract

According to the von Neumann–Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof of convergence is based on a known criterion in terms of the boundary spectrum.

Authors

  • Catalin BadeaLaboratoire Paul Painlevé
    Université Lille 1
    CNRS UMR 8524, Bât. M2
    F-59655 Villeneuve d'Ascq Cedex, France
    e-mail
  • Yuri I. LyubichDepartment of Mathematics
    Technion
    32000, Haifa, Israel
    e-mail

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